How did the byzantine empire continue the traditions of the roman empire?

the emperor was the head of the church.

they studied the knowledge of ancient greece.

the capital of the empire remained in rome.

they made latin their official language.

2686-2181 bce-- "egyptian civilization developed along the nile river in large part because the river’s annual flooding ensured reliable, rich soil for growing crops."

1069-664 bce-- "ancient egyptians developed wide-reaching trade networks along the nile, in the red sea, and in the near east."

well we know that it was fought between america and the united kingdom based on that i assume people consider the second war of independence because brtiain and england (uk)   the uk is made up of england and i assume thats why it was considered that